On the existence of positive solutions for periodic parabolic sublinear problems (Q1773479)

Summary: We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problems \(Lu=g(x,t,u)\) in \(\Omega\times\mathbb R\) (where \(\Omega \subset\mathbb R^N\) is a smooth bounded domain) for a wide class of Carathéodory functions \(g:\Omega\times\mathbb R\times [0,\infty)\to\mathbb R\) satisfying some integrability and positivity conditions.